##C#, <s>252</s> <s>247</s> <s>245</s> <s>232</s> 216 Bytes ##

The size is pretty bad compared to the other solutions but nevertheless...

    using System;using System.Linq;class p{static void Main(){var c="";var i=Console.ReadLine();var r=new Random();for(int b=0;b++<i.Count();){int d=r.Next(10);Console.Write((char)(i[b]+d));c+=d;}Console.Write("\n"+c);}}

This is my second ever answer to a codegolf and I'm quite a beginner considering C# so I'd appreciate to hear how to get it shorter :)

Ungolfed:

    using System;
    using System.Linq;

    class p
    {
        static void Main()
        {
            var c = "";
            var i = Console.ReadLine();
            var r = new Random();
            for (int b = 0; b++ < i.Count();)
            {
                int d = r.Next(10);
                Console.Write((char)(i[b] + d));
                c += d;
            }
            Console.Write("\n" + c);
        }
    }

- Saved 5 Bytes thanks to @FryAmTheEggman
- Saved 2 Bytes thanks to @theLambGoat
- Saved 7 Bytes by removing `static` from class p
- Saved 24 Bytes thanks to @milk